The sum of linear fractional functions problem has attracted the interest of researchers and practitioners for a number of years. Since these types of optimization problems are non-convex, various specialized algorithms have been proposed for globally solving these problems. However, these algorithms are only for the case that sum of linear ratios problem without coefficients, and may be difficult to be solved. In this paper, a deterministic algorithm is proposed for globally solving the sum of linear fractional functions problem with coefficients. By utilizing an equivalent problem and linear relaxation technique, the initial non-convex programming problem is reduced to a sequence of linear relaxation programming problems. The proposed algorithm is convergent to the global optimal solution by means of the subsequent solutions of a series of linear programming problems.